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 One 1 to Six 6's (Posted on 2015-07-01)
A standard six-sided die is to be rolled repeatedly until a side appears a number of times equal to its number. In other words until the n-th n appears.

Let P(n)=the probability the game terminates with the n-th n.

Find the distribution of n.

Feel free to generalize for m sides.

Warning: I have not managed this past m=4.

 No Solution Yet Submitted by Jer No Rating

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 Subject Author Date re: Solution for n=2 and 3, and some observations Charlie 2015-07-30 09:11:20 Solution for n=2 and 3, and some observations puzzlesrfun 2015-07-29 18:04:49 re(2): more results (11 and 12) Jer 2015-07-05 16:07:34 re: more results (11 and 12) Daniel 2015-07-04 09:45:05 more results Daniel 2015-07-03 21:01:10 re(5): computer aided solution (lots more) Daniel 2015-07-03 21:00:09 re(4): computer aided solution Charlie 2015-07-02 15:41:55 re(2): computer aided solution Charlie 2015-07-02 15:34:07 re(3): computer aided solution Charlie 2015-07-02 09:39:18 re(2): computer aided solution Charlie 2015-07-02 09:09:49 re: computer aided solution Jer 2015-07-01 22:17:03 re: computer aided solution Steve Herman 2015-07-01 18:48:00 computer aided solution Charlie 2015-07-01 17:00:33 m = 3 Steve Herman 2015-07-01 15:59:54
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